Solve for x

5/6 = x/4

Given:

The graphs of two parabolas.

To find:

The equation of the quadratic function with given graphs.

Solution:

(a)

The factor form of a parabola is

[tex]y=a(x-b)(x-c)[/tex]

Where, a is a constant, b and c are x-intercepts.

From the graph (a) it is clear that the graph intersect the x-axis at -1 and 3. So, b=-1 and c=3.

[tex]y=a(x-(-1))(x-3)[/tex]

[tex]y=a(x+1)(x-3)[/tex]            ...(i)

Put x=0 and y=3 because the y-intercept is (0,3).

[tex]3=a(0+1)(0-3)[/tex]

[tex]3=-3a[/tex]

[tex]\dfrac{3}{-3}=a[/tex]

[tex]-1=a[/tex]

Putting a=-1 in (i), we get

[tex]y=-1(x+1)(x-3)[/tex]

[tex]y=-(x+1)(x-3)[/tex]

Therefore, the equation of the parabola is [tex]y=-(x+1)(x-3)[/tex].

(b)

The vertex form of a parabola is

[tex]y=a(x-h)^2+k[/tex]

Where, a is a constant and (h,k) is vertex.

From the the graph (b), it is clear that the vertex of the of the parabola is at point (2,0) and y-axis is (0,8). So, h=2, k=0.

[tex]y=a(x-2)^2+0[/tex]

[tex]y=a(x-2)^2[/tex]            ...(ii)

Put x=0 and y=8 because the y-intercept is (0,8).

[tex]8=a(0-2)^2[/tex]

[tex]8=4a[/tex]

[tex]\dfrac{8}{4}=a[/tex]

[tex]2=a[/tex]

Putting a=2 in (ii), we get

[tex]y=2(x-2)^2[/tex]

Therefore, the equation of the parabola is [tex]y=2(x-2)^2[/tex].

Answer:

c

Step-by-step explanation:

there are 8 parts and 4 of them are red= 4/8

which simplifies to 1/2

Answer:

25.56% or $11.50

Step-by-step explanation:

I took it and put it in a sales tax calc.

Answer: x=4.373

Step-by-step explanation: Have a brilliant day mate -Lily ^_^

Answer:

x=4.373 (put a repetend at the top of three last digit)

Step-by-step explanation:

Combine rational expressions and isolate variable x

Answer:

I attached the graph below

Step-by-step explanation:

I started at the y-intercept, because it is where the line crosses the y-axis.  Then, I used rise/run for the slope (-5/3) and went down 5 units and right 3 units.  I connected the points to make the graph.  

Answer:

C . y(18x-9w-12) ..............

Answer:

35 meters per minute

Step-by-step explanation:

140 meters/4 minutes = 35 meters/minute

Answer:

35 meters per minute

Step-by-step explanation:

140÷4=35

35 meters per minute

Answer:

Step-by-step explanation:

Perpendicular lines have negative-reciprocal slopes

The line will have a slope of:

The equation is:

Use the pair (6, 2) to find the value of b:

The line is:

Answer:

ummmmmmmmm

Step-by-step explanation:

Answer:

12.7 is your answer

5 x 2.54 = 12.7

Answer and explanation:

The ratio 1:2 is different from the ratio 2:1. The ratio 1:2(one to two) means a comparison of two sizes; the ratio of one part of that thing to the ratio of two parts of that thing. Likewise, the ratio 2:1 is the comparison of two parts of a thing to the ratio of one part of the thing. For the ratio 2:1, we could say for example that for every two crushed tomatoes there is one tomato paste.

Answer:

FE= 20

Step-by-step explanation:

…......................

SAS

Step-by-step explanation:

GD = FE

3x + 5 = 4x

5 = 4x - 3x

5 = x

so, FE = 4x

= 4 × 5

= 20

Answer:

(-4, 1).

Step-by-step explanation:

For 180 counter clockwise rotation  (x, y) ------> ( -x, -y)

So ( 4, - 1) -------> (-4, 1)

The equation of the described circle is:

(x - 2)² + y² = 234

Remember that the equation for a circle whose center is (a, b) and has a radius R, is:

(x - a)² + (y - b)² = R²

Here the endpoints of the diameter are (17,-3) and (-13, 3), then the center is at:

( [17 - 13]/2, (-3 + 3)/2)

(2, 0)

And the radius is the distance between the center and any of these points:

R = √( (2 - 17)² + (0 + 3)²)

R = √234

Then the equation is:

(x - 2)² + (y - 0)² = √234²

(x - 2)² + y² = 234

LEarn more about circles at:

https://brainly.com/question/1559324

#SPJ1

Answer:

the answer is 6/7.

you're welcome.

Answer:

(0,8)

Step-by-step explanation:

Answer:

900

Step-by-step explanation:

because if you do 400×5m then that's 900

and that's how much work you did by just pushing 5 meters with 400 N

Answer:

Frances will complete 131,444,313 oil changes.

Step-by-step explanation:

919191 oil changes=777days

         ?                     =111111 days

=(919191*111111)/777

=131,444,313 oil changes

Answer: 175

Step-by-step explanation:

To determine the actual distance using the map scale of 1 inch = 50 miles, you would multiply the number of inches shown on the map by 50.

For this problem:  3   1/2 •  50 =   7/2 • 50 =  175 miles

The two cities are 175 miles apart.

Answer:

length of third side is 10 units.

Step-by-step explanation:

let x be the missing side

by pythagorus :

Answer:

The correct answer is 12

Answer:

the answetr is 3.5

Step-by-step explanation:

Answer:

4√5

Step-by-step explanation:

if this isnt the answer u needed lmk!!

Answer:

(0,4)

Step-by-step explanation:The y intercept is where the line passes through the y-axis.

Given:

12cm to 2.5mm

To find:

The simplified for of given statement.

Solution:

We know that,

1 cm = 10 mm

12 cm =120mm

We have,

12cm to 2.5mm

It can be written as

[tex]\dfrac{12\ cm}{2.5\ mm}=\dfrac{120\ mm}{2.5 mm}[/tex]

[tex]\dfrac{12\ cm}{2.5\ mm}=\dfrac{120}{2.5}[/tex]

[tex]\dfrac{12\ cm}{2.5\ mm}=48[/tex]

Therefore, the value of 12 cm to 2.5 mm is 48 or 48:1.

Answer:

a) 26; b) 5a+10;

Step-by-step explanation:

f(8)=3(8)+2

    =24+2

    =26

g(a+2)=5(a+2)

         =5a+10

Answer:

960 calories

Step-by-step explanation:

Answer:

there are 960 calories in 6 cups of cereal.

Step-by-step explanation:

Answer: 0.4

Step-by-step explanation: 3/4 - 1/3 = 5/12

converted to decimal: 5 ÷ 12 = 0.4

Answer:

3 /4 – 1/3 = 5 /12

Step-by-step explanation:

Calculation steps:

3 /4 –1 /3

=3 × 3 /4 × 3–1 × 4/3 × 4

= 9 /12 –4 /12

= 9 – 4 /12

= 5 /12